2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/116684We present an elementary, $L^2,$ proof of Fedi\uı's theorem on arbitrary (e.g., infinite order) degeneracy and extensions. In particular, the proof allows and shows $C^\infty,$ Gevrey, and real analytic hypoellipticity, and allows the coefficents to depend on the remaining variable as well.5ppAnalysis of PDEs35H10, 35N15text